How to get the distance from one vertex to other vertex along the normal polygon?
Use a dot product between the normal and the distance vector for the distance along normal.

import bpy
import numpy as np
from mathutils import Vector

# Use active object and active face in its mesh
ob = bpy.context.object
mesh = ob.data
normal = mesh.polygons[mesh.polygons.active].normal

# v1 is the origin point and v2 is moved to v1 along the active face normal
v1 = mesh.vertices[30]
v2 = mesh.vertices[31]

dvec = v1.co-v2.co
dnormal = np.dot(dvec, normal)

v2.co += Vector(dnormal*normal)